Conventionally, flexible dispensers of consumer products such as cosmetics, hair gels, condiments, beverages and liquid soaps are often produced with large standing caps and/or with multi-unit closure pieces. Multi-unit closure pieces have utilized a post-and-hole type mechanism. In these closures, closing of a hole in the cap is accomplished by insertion of a post on a base piece that attaches to the bottle. However, the manufacture of multi-unit closure pieces as well as large standing caps is relatively costly. For consumer products with high retail prices, the same methods can be satisfactory when the dispenser costs only a small fraction of the overall price of the packaged product. However, for many other products such as cosmetics, hair gels, condiments, beverages, and liquid soaps, or for packages containing small amounts of product, where dispenser costs become relatively significant, there is an increasing demand to reduce dispenser costs. What is needed then is an improved dispenser and closure that overcomes the shortcomings of prior dispensers.